To describe the detailed formulation of our method, we first present the IMU state vector and integration equations that are generally used in the inertial navigation.
Following [1]}, [2]}, [3]}, the IMU state is defined as:
\({\mathbf {x}} =\left[{^{G}_{I}{\bar{\mathbf {q}}}}^\intercal , ~{\mathbf {b}}^\intercal _{g}, ~{{^G}{\mathbf {v}}_I}^\intercal , ~{\mathbf {b}}^\intercal _{a}, ~{{^G}{\mathbf {p}}_I}^\intercal ~\right]^\intercal \in \mathbb {R}^{16}\) 
